The ratio of the volumes of two right circular cones is `1:4` and the ratio of their lengths of radii of the bases is `4:5` then the ratio of their heights is

Options

A. `1:5`
B. `5:4`
C. `25:16`
D. `25:64`

Explanation

Let the lengths of the radii of the bases of the right circular cone area `4x` unit and `5x` unit. Also , let heights of the two right circular cones are `h_1` unit and `h_2` unit.
So, the volume of the cones are `(1)/(3)pi(4x)^2h_1` cubic - units and `(1)/(3)pi(5x)^2h_2` cubic-unit.
As per question, `(1)/(3)pi(4x)^2h_1:(1)/(3)(5x)^2h_2` cubic - unit.
`rArr 16x^2h_1:25x^2h_2=1:4rArr (16x^2h_1)/(25x^2h_2)=(1)/(4)rArr (h_1)/(h_2)(1)/(4)xx(25)/(64)rArr h_1:h_2=25:64`
Hence the ratio of the heights of the two right circularf cones is `25:64` .
`therefore` (d) is correct.